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The Space Hose

by gutemine
Tags: hose, space
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Sep21-10, 03:10 PM
DaveC426913's Avatar
P: 15,319
Quote Quote by gutemine View Post
gutemine is actually a character from the Asterix comics book (I think in English she is called Impedimenta
Ah Impedimenta, yes. I remember her.

Always had a thing for Panacea myself...
Sep21-10, 03:23 PM
P: 59
Obelix has the same problem - so you are excused.

But Buzz is definitely the better Character for illustrating this concept - may the Toys (and Pixair) forgive me.
Sep22-10, 01:19 PM
P: 3
It's obvious that this theory has some flaw in it. All the "space elevator" concepts out there depend on one thing, a rigid wire which is held in orbit by a large mass. This large mass is critical because it holds the string taught.

Let's assume for a second that your idea works and you get the thing airborne and completely upright (this alone is very unlikely for reasons that I will describe later). So now you have a tube which is slightly fluttering around in the air (because remember you chose TURBULENT airflow. This is why your wild wacky inflatable tube man flutters in the air instead of standing straight like you would like him to, it's because of the turbulent flow. If wild wacky inflatable tube man were using a high viscosity fluid such as water, he would not dance because of the LAMINAR reynolds number). But i'll be nice. Let's assume that you figure out a way to get the thing stable and upright, I donno you inject some laminarizing particles... or something... But anyway it's straight, it's upright and it's stable.

So now you look up at the top of your glorious hose and you realize it's curving... but how can this be? There's such a mighty air pressure! It's for the same reason that poster #4 said. You must impart SIDEWAYS velocity. Vertical velocity just doesn't cut it. Imagine you attach a string to a frisbee and throw it, that string is going to twist with the frisbee. That's because the tension and centrfugal force, and the sideways strength of the fibers in the string just cannot overcome the change in angular velocity. If you had a big steel rod and you spun it, it would STILL BEND (a little bit, but imagine that big steel rod is 80,000 ft long and you get the idea).

Ok so let's assume that you get the thing upright, stable, and you somehow reinforce it so that it's not bending under its own weight (I have no idea how you're going to do this, but let's assume you get it to not bend). So now you're like OMG I just erected a huge tube, what a glorious monument to my awesomeness!!!!! So then you try to blow a small satellite up your tube. You stick it in the bottom and start blowing. You notice that as soon as it's about 100 ft above the ground that your perfectly straight tube begins to bend again, but in a V bend (because we assumed that your tube was erect under its own weight). So now ur like ok I'll just increase the air pressure (at which point I guarantee you will blow a hole in whatever material you are using, even CNT's).

The core problem with your space hose is connected to the conservation of angular momentum. You cannot simply send an object into a state of higher angular momentum without robbing that angular momentum from something else. That's what the big rock at the top of the space elevator does. We have to capture an asteroid with a lot of angular momentum so that we can slowly impart its momentum to the satellites we send up there. The elevator cable doesn't work like a normal elevator cable, it must strain SIDEWAYS. The upward force is TRIVIAL compared to the sideways force that must be imparted by the cable on the satellite. This is why the vast majority of a rocket's flight is on its side and not upright.
Sep22-10, 01:37 PM
DaveC426913's Avatar
P: 15,319
Despite z06_pit's heavy sarcasm, he has a point.

He's touched on something that's been bothering me too. Even with the space elevator, by the time you reach GEO, you are moving at a substantial velocity around the Earth (orbital velocity, in fact). This transverse velocity does not come free. As he says, it must be imparted upon the rising payload.

In the space hose, you don't have that rigid structure's ability to impart transverse velocity on its payload. You'll have to account for that.
Sep22-10, 01:57 PM
P: 3,387
I have to say, Z06_Plt post is one of the best in this thread. I think the sarcasm is somewhat heavy, but necessary in so far as it reinforces the critical points which cannot be avoided and really do need addressing at this early stage. Solving one problem at a time may seem like a good idea, but without forward planning it can mean you end up back tracking and having to perform multiple redesigns (which can be costly and time consuming).
Sep22-10, 02:16 PM
P: 59
I don't have a problem with sarcasm and critics - I desperately need it to to make it work.

But let me try to adress the feedback we got:

Actually properly fllying in the typical steroid with a large mass and rendevouz it with the tether is quite a complex thing and there have been already papers written on this and lots of compuer simulation done - really scaring, because it is like catching a huge baseball with a thin string - if the ball introduces to much stress because he needs to be accelerated by the hose you get a terrible effect, if it is too fast the stress in the tether to slow it down could blow the whole thing. And our current technology is not that great in flying asteroids BTW.

So the whole counterweight thing is not such a great solution as it actually looks at the first glance (it just makes you scream louder for carbon nanotubes, and hope that they will be also flexible) Remember I looked first into the problems of the existing concepts before creating my own.

Actually the slides on the space hose contain at least some thoughts about the velocity bowing problem:

The good thing for the Space hose is that 100km is only very very much less then 36000km - and because centripedal force F=mv/r you the difference is even MUCH smaller. Actually you don't have orbital speed either (which would be a nightmare due du the and a diameter is 720x smaller (72000km vs. 100km). So you have to instantly drop quite a number of zeros in your worries.

The real speed difference top to bottom is in the slides - it is 26km/h or a moderate 7,27m/sec (which is about 2x the blowing speed - and I already commented multiply that something like 10m/sec is much more likely if you need extra weight for strengthening and want to have optimal blowout speed).

But anyway, this means that it will take approximately 2min to move the top 1km (1% of height). Hence you are right - if erected straight up it will fall - pretty fast.

On the other hand you are absolutely right, if the hose hose has same angular speed there should be no real problem out of the speed difference, and even some bowing. If you erect the hose in a day as suggested (but let's take the 8h that the air would travel trough when you blow into with 3,5m/sec - which is not correct because due to gas expansion by decreasing pressure the air will be much faster). Then you would have 8h to accelerate the top of the hose to 7,2m/sec - Which gives you 7,2/8/3600=0,00025m/s if we assume continuous acceleration. With the air blown out on the top in 8h (rememmber we talk about a minimum of 618m/h on the bottom, which is 625x618m at the top) you can easily produce this very weak acceleration to give to the entire hose (the 283kg) the proper angular speed. And yes, it will curve during erection, and probably even stay that way - that is the great thing about a hose - it can do this - as long as it is strengthened to hold the remaining pull forces.

But you are right - you could see the entire hose as a 100km long wall effect. If you take a wind tunnerl and hang a diametric wool string into it which is lose enough it will form something very similar to the parabolic velocity curve the gas is showing when flowing laminar. But it will be ONLY pull forces in the entire wool string.

Now let's try to find out how big this pull force could be. I'm a bad guy and hate integrals (to get the exact number). So let's be lazy and put the entire mass of the hose (283kg) at 100km height:

radius=6478000m (6378km earth radius + 100km hose)
speed=2*6478000/24/3600=471m/sec (the famous 0,4km/s that you can save when starting your rocket east at the equator - reducing orbital speed difference from 7,8km/s to 7,4km/s)

F=283*471/6478000=9,7N - now I'm really scared :-)

The hose at 250mm diameter and 0,004mm thickness has 250*pi*0,004=3,14mm

At 20N/mm tearing strength this means the hose can hold about 63N This is NOT much, but already could hold this centripedal force without the planned Dyneema string strengthening. BTW this is the reason why industrial PE foil is sold in 12/25/50micrometer thickness - because then if plastic bags are made out of the hose your grocery pruchases are save - because 63N is not really what you get when doing family shopping (=6kg). I simply have choosen the 0,4 so that the 100km is a neat roll of foil, and that I can easily add strengthening without blowing the friction lift concept by needing a thunderstorm to hold it upright. A hose up to maybe 1ton, can be held with a moderate airflow in my understanding which would produce pressures which are handable by the suggested materials.

And regaring the wiggeling because of turbulent flow. You are right, but a hose with a reasonable pressure surpluss is also the perfect damping device, especially when it is smooth and long. Because both the hose and the air are not heavy and hydrostatic pressure is balanced from outside I'm not sure if this would be that bad as you suggest. The air petrol station toy is not only wiggeling because of turbulence, it is because of the desing to reduce the diameter so that airflow increases, presure goes down until the outside pressure is bigger and the hose bows sidewards, then the pressure increase due to the closed hose puts it upright again. So it is designed as a kind of penumatic pendulum.

Try the same with a fixed diameter hose and a diffusor on top for generating pull forces. And even a fully turbulent airflow in a hose has a thin laminar piece at the walls of the hose (because of the lower frequency there). Hence the turbulences are not really scaring me - it is the increasing flow speed (if it is not compensated by diameter adaption, diffusors,..) which theoretically goes beyond the speed of sound. But nobody commented on this so far.

Sep22-10, 02:30 PM
DaveC426913's Avatar
P: 15,319
Quote Quote by Z06_Plt View Post
So then you try to blow a small satellite up your tube. You stick it in the bottom and start blowing. You notice that as soon as it's about 100 ft above the ground that your perfectly straight tube begins to bend again, but in a V bend (because we assumed that your tube was erect under its own weight). So now ur like ok I'll just increase the air pressure (at which point I guarantee you will blow a hole in whatever material you are using, even CNT's).
On the other hand, let's keep in mind that the satellite only weighs 9g (yes, nine grams). That's a pretty negligible amount of mass to toss about.

The N-prize rules are simple deliberately. Scaling challenges are pointedly outside the scope of this project.
Sep22-10, 02:39 PM
P: 59
If the relationship N-SAT size to hose diameter is less then something like 10 there should not be a real problem - it will simply move to the center of the flow where the highest speed occures. And even when it would touch the walls, the force of a tangential impact is small and a hose under surpressure is almost perfect elastic. It would maybe mage some strange drumm sound while beeing blown upwards. Or we make it intentionally tach the wall with a kind of parachute with holes.

But the blowup behaviour of the SAT and the impact of turbulent flow is something relatively easy to test. You would only need to buy a few hundred meter of foil and try it out, Because of the weight of such a hose beeing in the 10kg range a simple model plain propeller and engine could already do all the blowing needed.

Somebody volunteering to try it out ?

But be aware you would need at least a very simple stabilizing diffusor on top or you will fail erecting it when going beyond a few meters.

I think the N-prize rules are pretty clever - they remove some problems and create new ones - but just building a small Saturn V or a small Space Shuttle would be boring, woudln't it ?

So I think the lack of scalability is the opportunity of the whole thing. Even for the space hose -10" diameter is peanuts, but more then enough for such an N-SAT. And actually it is exactly this very strange lift/weight/power/strength ratio which seem to make such a hose concept feasable - in the first run targetted at this purpose. Finally if it works at that scale you can try to make a real lift device for more sensemaking purposes. And yes, Paul did this intentionally to force the people on new ground, instead of trying to dig the same old holes all over again.

Sep22-10, 02:45 PM
P: 3
Capturing an asteroid is difficult and nearly impossible. Let's face it, if a huge asteroid comes that close to Earth that we can capture it, we are not going to be like "oh it's a friendly asteroid that we can use to build a space elevator". It's going to be like "My fellow Americans, we are honestly f****d. I am ordering that we nuke the thing out of our path and ask questions later". So I am by no means advocating the asteroid idea.

But to be honest you really don't need an asteroid, you just need a large mass at the top of your hose. Spiders don't build a web to support their own mass all at once, they don't just projectile crap out a web. They build it one strand at a time, get each strand to hold its own weight and then aggregate the strands to hold the spider's weight. I believe that the solution is going to come from a similar way of thinking. Granted, we are talking about each string as a multi-million dollar satellite launch, but it's an exponential growth model we're dealing with. (I'll explain more about this a little later)

Your hose idea is good except for the fact that you are lacking a way to impart angular momentum. You can get the vertical momentum with the air stream, there is no problem with that. You're going to be dealing with a pipe friction loss bigger than a naked fat lady on a metal playground slide, but granted, it's entirely feasible. And to be honest, it's a lot simpler than a robotic-laser-powered-crawler thing that they're putting all their eggs in currently. So all you need is a way to get angular momentum.

Let's say you launch a rocket. This rocket has a string tied to it, quite literally. It's made out of some high tech material, CNT's, Kevlar/cupronikel fibres, aggregated nanofibres, whatever (I recommend Nylon, you'll see why if you do some research). But regardless, it's a string tied to a rocket, nothing theoretical there. Launch the rocket into geosynchronous orbit and release the string. This string has a small weight on the end of it (emphasis on small, it's just big enough to pull the string taught and overcome air currents in the atmosphere). You throw the string out and send the rocket home. So now you have a string able to hold its own weight, in space, with a weight attached. You do this about 10 times, tying the strings together each time. (Yes I know that the orbits of the strings are going to degrade rapidly due to air friction from the lower atmosphere portion of the string. But this can be solved with a small, temporary thruster on the end of the string)

Now you launch your hose. Tie it onto the strings and now you have a means to transport small amounts of mass into space. But now let's say you don't use air... let's say you use methane and air. And you have a small nozzle at the top of your hose. Now what do you have? You have a rocket which is able to impart angular momentum on the string and whatever you send up. Then you fire another rocket up there towing your BIG hose. Now you have rocket engine up there to keep the big hose taught, and you have a means to transport small satellites and other cargo through the big hose.

Cut the small weights (from the very beginning) loose and you're in business.

I find the sarcasm/mocking makes my posts/papers easier to read. And, contrary to popular belief I actually like gutemine's approach on this, he's got some solid theoretical backing. Perhaps some of my ideas can help you hone your theory down to something usable. Because let's face it, do you really want to win the X (or N or whatever) prize on a technicality? A technicality is not going to help anyone. If you can manage to get something into GEO orbit with this thing, that's worth a hundred times more than just getting some little thing suspended at 100km.
Sep22-10, 03:01 PM
P: 59
As the slides say, rockets are boring, but they work.

Unfortunately there is no such string which the rocket could pull - it would first tear from the acceleration and then from its own weight. The whole idea of the hose is to do everything slow and under control. Erecting it in a day, blow with jogging speed (maybe bicycle speed, remember friction goes with v). Using ultra light material to keep the forces and masses low.

As I said at the halfbakery. If you have to build something in the desert - then use SAND!
We live at the bottom of an ocean of air - so it is the logic construction material!
I just followed this logic to the extreme.

Continuously supporting the weight is actually the only real new thing within the whole concept.

Instead of using a wing to create lift you simply use friction - as the slides say, the whole thing is a dumb circular flag blown from the inside - which should make it work also in vacuum.

PS: The entire problem with ballons running our of steam beyond 30-40km simply annoyed me - you get 1/3 of the 100km almost for free, and then the driver kicks you out of the bus and you have to wait for a rocket ? So I decided to start my own bus/hose :-) And this is also the reason why I dislike the ballon+rocket or even hose/tower+rocket conecepts. If I have air blowing out on the top Bernoulli and de Laval should be everything you need to even get the lacking orbital speed (again for an N-SAT - not for a space shuttle)

PPS: My background actually is poor on such things (I have other hobbies too), but I'm using it as good as a can. And as I already said - the math and pyhsics behind this is not something which should not look familiar when you had a good physics teacher at highschool. And so far we did a good job in debugging the concept and analyze its problems or try to get an idea how big they really are. If you solve all small problems usually the big ones are gone too is one of my favoirite sayings. And as the original post says - N-prize is also about the entertaining value - so I don't have a problem if we have fun together.

Sep22-10, 03:21 PM
P: 3
Quote Quote by gutemine View Post
Unfortunately there is no such string which the rocket could pull - it would first tear from the acceleration and then from its own weight.
Rocket acceleration is less than 3g at all times.

Breaking under its own weight is a different story entirely. However, if you use nylon, this problem gets a lot simpler.

Quote Quote by gutemine View Post
the whole thing is a dumb circular flag blown from the inside - which should make it work also in vacuum.
Quote Quote by Niel Armstrong
Oh **** this circular flag doesn't blow on the moon! I better stick a rigid wire in there for support.
Granted, Col Armstrong is referring to different situation than yours, but I just thought that it was funny, considering your choice of words.

What you described is different than a circular flag, there are many reasons why it is different than a circular flag. The most prominent of which is the fact that a "flag" is generally horizontal, and a "tube" is generally vertical. The second most prominent of which is the fact that when you extend this tube such a distance, the frictional losses prevent air from reaching the other end without manual pumping. This pumping changes the problem from that of friction to that of pressure/structural rigidity.
Sep22-10, 03:54 PM
P: 59
A flag is also fighting gravity - hence the wording is not that bad :-)

Even Dyneema which is already pretty strong at a reasonable price/strenght ratio is able to hold already 300-400km of its own weight. But if you attach it to a hose which is able to hold the weight you can even avoid this problem to some extent.

If you would have a rocket with enough fuel to stay stationary in 100km height above ground you could already now hang a Dyneema string down and let climb everything which the rocket is able to hold as extra weight.

And there are rockets pulling cables - ask the US army - they call this an anti tank weapon and use the wire for steering it. But this concept runs out of usability beyond a (few) km or something.

Actually the picture of the Space Elevator climber challenge with the helicopter holding a 1km steel cable was also a big inspiration for me.

Regarding the friction force. The formular I used is designed for a horizontal PIPE. And the pressure loss it reports is only 0,6bar over 100km. Well, the problem ist that the formular is not designed for this, but theoretically if you would blow into such a pipe with 0,6 bar at this relatively low speed (3,5m/sec is a soft breeze if you do some sailing) the whole pressure should be eaten up on the end and you would blow out at 1 bar (which you would do when the end is open in any case).

If you now would use a hose instead of a pipe nothing really changes, if the hose is blown trough at the ground, except that you suddenly blow out in almost vaccum (100Pa) and instead of transferring all the friction force to the ground where the pipe was laying it will pull the hose upwards - against its own weight. I just tried to find what would be needed to reach an equilibrium of these 2 forces.

if you put the pipe/hose upright you simply have to add hydrostatic pressure (at least Mr. Bernoulli saiys so), Which for air is not a real problem, because the air outside does the same and hence the pressure should be always balanced. But I'm not even sure in what way this friction force would be transferred to the hose - blowing with extra speed (almost 300m/s as the slide suggest), or with the 0,6bar surpressure (bad but a Dyneema wrapped hose could still hold this) plus the suggested 3,5m/s ? But it is an open hose not a pipe, so normally there should be no surpressure except from the diffusor ?

BUT what is even more strange is that when you move 1m from bottom to top it will dramatically expand (would be 1000x in case temperature would be the same, but temperature on ground is 20 degree and in 100km it is -90 degree of celsius, hence expansion is only 625x). Friction is dependent on dynamic viscosity (dependant on temperature and density of the gas) and on the speed of flow. So friction in general is likely to go up because v should win. Which would mean the upper part of the hose should eben get more friction and pull (unless you change the diameter). And the friction is even worser, if pressure drop occures due to it, it should create additional speed increase (Bernoulli - remember). But if you get so much speed from expansion already you don't need to feed it all at the ground in my understanding, and there should be an equlibrium of blowing an friction.

But it is even more confusing, after 100x expansion at about 50km height (there you have approximately 1000Pa pressure outside) the flow would reach the speed of sound without friction. And after this if you reduce the pressure further (which the atmosphere does for you) the speed would go further up, and because of the sonic border the hose would not even know that it is open or not. This is scaring, I intentionaly wrote in the slides the crazy question about a fixed diamter de Laval Nozzle :-)

On the other hand if friction really works and the speed stays in a sensemaking range, worst case would be that the friction converts to heat, which means further expansion and chimney effect in the hose giving also upwards flow.

Do you understand now that it is NOT that easy to say after a few kilometer it doesn't matter if the hose is open or upright, it will be like blowing into a kind of huge tank which at the end is only a crazy way of heating the whole device ?

So the real probably will be somewhere in between - air flow and supressure and expansion and friction, and ...

Because expansion and continuity law are still on our side, and as long there is flow you have friction - which always creates a force on the wall/hose which should be able to keep its weight if properly desinged ?

And remeber the whole thing is 100km long, so ALL speed and pressure gradients are extremely moderate (that's why I suggested a finite element calculation with 100m pieces in a spreadsheat to get some more accurate results on the speed and pressure gradient), this is not really the typical supersonic wind tunnel with extreme forces. I just decided some basic parameters like diameter and thickness and did some math - if we would have a proper model of the flow inside you would need to iterate it for finding the optimal parameters which could also include diameter changes to control the velocity - but then you would be in trouble when erecting the hose, etc.

Actually the whole thing is much more complex then it looks at first glance so saying yes or no is not that easy then I thought.

Which brings me back to my confusion and the reason why I have put it on slides and asked open and honestly for help !

Sep25-10, 03:59 AM
P: 59
Hi !

Just a small update so that you don't think I have forgotten you or got completely lost:

I have spent the last few days to build a spreadsheet which calculates the standard atmosphere from 0 to 100km in 1km pieces, and then applied the formulars of the slides to these pieces to better understand what happens in the hose.

Then yesterday (during my morning shower!) I actually found out why I had so big problems getting sensemaking results:

It was a typical border value problem. Actually I always tried to calculate from bottom to top, but it is much easier to do it top to bottom, because there you simply define the maximum blowout speed (for example speed of sound to prevent the hose going supersonic) and the needed surpressure required to hold the payload and provide sufficient pull power to keep the hose stable.

Then you calculate the pressure loss of the resulting flow 1km down, add it to the atmospheric pressure there and the requested surpressure and get with ideal gas law a new density there, and hence a new flow speed because of continuity law. This means a new Reynolds number and a new viscosity and Lambda which means you have all the starting values for the next 1km and so on.

The pressure and blowing speed at the bottom are then a simple result of this iteration down and not the other way around. Because you can change pressure and blowing speed at the bottom in a relatively wide range depending what pump/fan you use this is not really a problem, and much better then choosing them and then get weird results at the top and within the hose.

Then you calculate the speed of sound at all these points to check that nowhere the air flow is faster. When you then have the flow and pressure gradient of the entire hose you can calculate the tension forces in the hose and can check if the PE foil and/or Dyneema strength can hold it.

If you blow out at the speed of sound this also becomes a kind of event horizon, meaning the hose doesn't care/know what the diffusor afterwards does, if you add a de Laval nozzle to blow out supersonic, turn the air flow downwards to generate lift, etc.

Then you are done and have a Spreadsheet where you can start playing with different blowout speeds, diffusor pressures, different foil thickness, hose diameters,... to find the optimal hose.

I will polish the spreadsheet a little bit more so that everybody can use it and then probably tomorrow you can play with it. There are some quite interesting findings already from what I tried out.

So actually the formulars and the math was not that bad (and there was no real critics from you on this either), but the USAGE was simple a little bit dumb and I should have tried it the way I suggested already earlier instead of trying to enter 100km in a single formular which allows to get an idea if it would work, but produces only consfusion on how.

Thanks for your patience with me!

Sep25-10, 09:24 AM
DaveC426913's Avatar
P: 15,319
Cool. I'd be interested in your first take on fan speed/pressure.
Sep25-10, 10:58 AM
P: 59
Quote Quote by DaveC426913 View Post
Cool. I'd be interested in your first take on fan speed/pressure.
Well, the first key finding was that actually the blow speed at the bottom is lower (which is logic if you limit the head to 270m/sec which is approximately the speed of sound at -90 degree of Celsius), but you need a slightly higher surpressure to keep the whole thing stable (approximately 500-1000 Pa). This helped a lot to sort out the do I feed flow speed or surpressure at the bottom question which I never could sort out when I tried to calculate from there (predicting these 2 variables at the top is much easier and logically).

Funny is that the top contributes most of the pull forces even without the diffusor, which is good for extra stability. I already assumed this (because of the v of the friction forces, but I didn't have any idea to what extent)

I'll see if I can warp it up and add some comments and colors for the changabel fields until this evening than you can play with it yourself.

Having such a 'virtual Space Hose' where all the parameters are changeable is pretty funny, and it even gives interesting results like pressure waves on top if the surpressure is too low, or how low you can bring the hose tensions down before it fails to stay errect (approximately 100N/mm - which is not so far away from plain PE)

As I already mentioned I'm doing also some open source software development as another hobby so as soon as I found the formulars on how to calculate the Standard Atmosphere model from the definitions it was not so diffucult to build a Spreadsheet out of it.

Then I found another Webpage where you can calculate air viscosity for all temperatures:

It took me almost 1 hour to get all 100 viscosities for the model, but I was too lazy to try to reverse engineer the math for this too :-)

From these two raw inputs you have everything needed for the pressure loss calculation at all heights, and then the fun started when putting it together.

Sep25-10, 11:35 AM
P: 59
One more question on the wind - I found a nice picture on this (see attachment)

Would this mean that a hose with pull from top would actually form more or less such a bent curve ?

Because I would like to include also the pull force calculation into the excel, and for this I need a better understanding of the distribution of the wind force on the lower end of the hose.

Attached Thumbnails
Sep26-10, 11:24 AM
P: 59
Damned - I still have problems with my Excel and the discrete calculation steps because now I have a circular reference.

If I go 1km down this means that the pressure on the bottom should be the one at the top + pressure loss from friction + hydrostatic pressure of the 1km of gas.

The problem is that hydrostatic pressure is dependant on the density, which is resulting from the pressure from bottom to top (if I asume that temperature is always aproximately outside temperature of the standard atmosphere) = circular reference. Now I understand why the books are saying this is a differetial equation with an integral which is only numericially solveable - if at all :-(

And if I try to overcome this by simply taking the previous density as I did until now the result is underestimating pressure, which makes the numbers look good, but then the model is invalid beyond the top few kilometers of the hose, because only there density and hence hydrostatic pressure is low enough to allow such a simplification. So calculating top to bottom was a good idea, but gives wrong results at the bottom because of the discretisation. This is also the reason why going from bottom to top produced too high numbers on top.

But problems are there to be solved, and input is welcome ;-)

Nov4-10, 04:13 PM
P: 5
Is the "space hose" thread over?

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